Introduction To Asymptotics - A Treatment Using Nonstandard Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction To Asymptotics - A Treatment Using Nonstandard Analysis write by Douglas S Jones. This book was released on 1997-01-16. Introduction To Asymptotics - A Treatment Using Nonstandard Analysis available in PDF, EPUB and Kindle. Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hyperasymptotics as well as uniform asymptotics. There are many numerical examples to illustrate the relation between theory and practice. Exercises in the chapters enable the book to be used as a text for an introductory course.
Introduction to Asymptotics
Introduction to Asymptotics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Asymptotics write by Douglas Samuel Jones. This book was released on 1997. Introduction to Asymptotics available in PDF, EPUB and Kindle. "A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods".Mathematical Reviews"As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics".SIAM, 1998" it is an excellent book that contains interesting results and methods for the researchers. It will be useful for the students interested in analysis and lectures on asymptotic methods The reviewer recommends the book to everyone who is interested in analysis, engineers and specialists in ODE-s"Acta Sci. Math. (Szeged), 1999
Nonstandard Asymptotic Analysis
Nonstandard Asymptotic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonstandard Asymptotic Analysis write by Imme van den Berg. This book was released on 2006-11-15. Nonstandard Asymptotic Analysis available in PDF, EPUB and Kindle. This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the theory are presented via concrete examples, with many numerical and graphic illustrations. N
Lectures on the Hyperreals
Lectures on the Hyperreals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on the Hyperreals write by Robert Goldblatt. This book was released on 2012-12-06. Lectures on the Hyperreals available in PDF, EPUB and Kindle. An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.
Asymptotics and Mellin-Barnes Integrals
Asymptotics and Mellin-Barnes Integrals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotics and Mellin-Barnes Integrals write by R. B. Paris. This book was released on 2001-09-24. Asymptotics and Mellin-Barnes Integrals available in PDF, EPUB and Kindle. Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.
